Question

A basketball player scored $31$ times during one game. he scored a total of $52$ ​points, two for each​ two-point shot and one for each free throw. how many​ two-point shots did he ​make? how many free​ throws?

Answer 1

Finding number of two-shots and free shots:

Let $x,y$ be the number of two-shots and free shots then total number is given to us $31$ so,

$x+y=31$

Also, two points for two-shots and one for free throw with total points scored as $52$ we get

$2x+y=52$

Solving both equations using substitution method we get,

$$\begin{gathered} 2x+31-x=52 \\ \Rightarrow x=21 \end{gathered}$$

and, $$\begin{gathered} y=31-21 \\ y=10 \end{gathered}$$

Hence, number of two-shots and free shots were $21,10$